MinT - Best Known (138−64, 138, s)-Nets in Base 9

Best Known (138−64, 138, s)-Nets in Base 9

(138−64, 138, 320)-Net over F₉ — Constructive and digital

Digital (74, 138, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 69, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(138−64, 138, 356)-Net over F₉ — Digital

Digital (74, 138, 356)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−64, 138, 20823)-Net in Base 9 — Upper bound on s

There is no (74, 138, 20824)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 485025 906084 862987 812159 498192 424609 879879 467310 769495 368150 176142 428669 168074 015813 294721 448813 151784 692863 762650 053777 738387 892225 > 9¹³⁸ [i]